Details

Autor(en) / Beteiligte

• Holden, Helge
• Karlsen, Kenneth H.
• Mitrovic, Darko
• Panov, Evgueni Yu

Titel

STRONG COMPACTNESS OF APPROXIMATE SOLUTIONS TO DEGENERATE ELLIPTIC-HYPERBOLIC EQUATIONS WITH DISCONTINUOUS FLUX FUNCTION

Ist Teil von

• Acta mathematica scientia, 2009-11, Vol.29 (6), p.1573-1612

Ort / Verlag

Elsevier Ltd

Erscheinungsjahr

2009

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Under a non-degeneracy condition on the nonlinearities we show that sequences of approximate entropy solutions of mixed elliptic-hyperbolic equations are strongly precompact in the general case of a Caratheodory flux vector. The proofs are based on deriving localization principles for H-measures associated to sequences of measurevalued functions. This main result implies existence of solutions to degenerate parabolic convection-diffusion equations with discontinuous flux. Moreover, it provides a framework in which one can prove convergence of various types of approximate solutions, such as those generated by the vanishing viscosity method and numerical schemes.